The probability of A is 0.4. The probability of AC is 0.6. The probability of (B | A) is 0.5, and the probability of (B | AC) is 0.2. Using Bayes’ formula, what is the probability of (A | B)? A) 0.625. B) 0.125. C) 0.375.
A
Hi, This is my slightly long winded but hopefully helpful attempt at an intuitive answer. The answer is A) 0.625 I always try to approach probability questions with a diagram or drawing. In this case I have drawn a box and divided it into four parts. I have labelled the columns A & AC and the rows B & BC. This might sound odd but I also try and substitute some sort of thing, such as people in for the probabilities to make it more intuitive. So… 40 people will be A and 60 will be AC as per the probabilities noted in the question. Of the 40 people who are A, there is a 50% chance (20 people) they will be "B given that they are A "and a 50% chance (20 people) they will be “BC given that they are A”. Of the 60 people who are AC there is a 20% chance (12 people) they will be “B given that they are AC” and a 80% chance (48 people) they will be “BC given that they are AC”. From this we can see that there will be 32 people who will be B. Of these 32 people who are B, 20 will be A and 12 will be AC. This gives us a final answer of 20/32 or .625
soddy’s method works(I am always for logical stuff!) but in exam you may just want to apply the formula to save time P(A/B)=P(AB) / [P(A)P(B/A) + P(AC)(P(B/AC)] where P(AB)=P(BA)=P(B/A).P(A) AC= A compliment just substitute the values!
soddy1979…that is a great explanation. I like the use of the box divided into four parts. I prefer to use the tree diagrams and then use the formula: P(A | B) = P(A and B) / P(A and B) + P(AC and B) This equals 0.2 / 0.2 + 0.12 0.625 Answer A
At the end of the day it’s whatever works for you! I couldn’t get my head around Bayes for a long time… I was then shown how to slot the different probabilities into a diagram and it started making perfect sense to me. Best of luck everyone! Hope you all have a productive weekend.
A
soddy1979 can you please try to explain it in a bit more details if you can?? I would really appreciate that!
I just never got this and just skipped it completely when reviewing. At most this is one question on the exam. Luckily it wasn’t on the exam but even if it was it wouldn’t have made a difference. This is a classic case of diminishing returns, the effort spent on understanding this just isn’t justified by the reward.
Using the total probability rule, we can compute the P(B): P(B) = [P(B | A) × P(A)] + [P(B | A’) × P(A’)] P(B) = [0.5 × 0.4] + [0.2 × 0.6] = 0.32 Using Bayes’ formula, we can solve for P(A | B): P(A | B) = [P(B | A) ÷ P(B)] × P(A) = [0.5 ÷ 0.32] × 0.4 = 0.625
Hi sweetiecfa, There is a google group at the below link. I will post some further information on Bayes in the next day or two to it. If you are not a member of the below yet you can request to join and someone will approve you. http://groups.google.com/group/cfa-email-study-group
Hi, Sreeharimenon I have doubt, about calculation P(B) P(B) = [P(B | A) × P(A)] + [P(B | A’) × P(A’)] , I am ok, but why we assume that P(B | A’)=P(B|AC)=0,2 ?? Mayby I am wrong, but please correct me Thanks for help
Original post wrote it as AC. It should be Ac, where the c is superscript. Or A’.
Thanks 4Tay, Now, that’s make sens
Hate Bayes